def conv2d(smaller, larger):
"""convolve a pair of 2d numpy matrices
Uses fourier transform method, so faster if larger matrix
has dimensions of size 2**n
Actually right now the matrices must be the same size (will sort out
padding issues another day!)
"""
smallerFFT = numpy.fft2(smaller)
largerFFT = numpy.fft2(larger)
invFFT = numpy.ifft(smallerFFT*largerFFT)
return invFFT.real
def getimage(self,z):
'''
:param z: the Zernike vector in microns, starting from Z=2 (tip)
z[0] is seeing in arcseconds
:return:
'''
#COMMON imagedata, uampl, filter2, seeing
fact = 2.*np.pi/self.alambda
nzer = len(z)
phase = np.zeros_like(self.zgrid[0]) # empty array for phase
for j in range(1, nzer):
phase += fact*z[j]*ztools.zernike_estim(j+1,self.zgrid)
# # log.debug('GETIMAGE: %s %s'%(phase[0],phase[-1]))
# exit(0)
uampl = np.zeros((self.ngrid*2,self.ngrid*2),dtype=np.complex)
#uampl = np.complex(tmp, tmp)
self.uampl = uampl
uampl[self.inside] += np.cos(phase) #,
uampl[self.inside] += (np.sin(phase)*np.complex(0,1))
#uampl[np.bitwise_not(self.inside)] = 0.
self.seeing = z[0]
#--------- compute the image ----------------------
# imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(uampl,self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2)),self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2))**2.
imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(uampl,self.ngrid,self.ngrid)),self.ngrid,self.ngrid))**2.
if (self.sflag > 0): # exact seeing blur
filter2 = np.exp(-2.*np.pi**2*(self.seeing/2.35/self.asperpix/2/self.ngrid)**2*self.r**2) # unbinned image
imh = np.abs(np.fft2(ztools.shift(np.fft2(imh),self.ngrid,self.ngrid)*filter2))
impix = ztools.rebin(imh,(self.fovpix,self.fovpix)) # rebinning into CCD pixels
else:
rr = ztools.shift(ztools.dist(self.fovpix),self.fovpix/2,self.fovpix/2)
filter2 = np.exp(-2.*np.pi**2*(self.seeing/2.35/self.ccdpix/self.fovpix)**2*rr**2) # binned image
impix = ztools.rebin(imh,[self.fovpix,self.fovpix]) # rebinning into CCD pixels
impix = np.abs(np.fft.fft2(ztools.shift(np.fft.fft2(impix),self.fovpix/2,self.fovpix/2)*filter2)) # Seeing blur
self.filter2 = filter2
return impix/np.sum(impix)
def getimage(self,z):
'''
:param z: the Zernike vector in microns, starting from Z=2 (tip)
z[0] is seeing in arcseconds
:return:
'''
#COMMON imagedata, uampl, filter2, seeing
fact = 2.*np.pi/self.alambda
nzer = len(z)
phase = np.zeros_like(self.zgrid[0]) # empty array for phase
for j in range(1, nzer):
phase += fact*z[j]*ztools.zernike_estim(j+1,self.zgrid)
# # log.debug('GETIMAGE: %s %s'%(phase[0],phase[-1]))
# exit(0)
uampl = np.zeros((self.ngrid*2,self.ngrid*2),dtype=np.complex)
#uampl = np.complex(tmp, tmp)
self.uampl = uampl
uampl[self.inside] += np.cos(phase) #,
uampl[self.inside] += (np.sin(phase)*np.complex(0,1))
#uampl[np.bitwise_not(self.inside)] = 0.
self.seeing = z[0]
#--------- compute the image ----------------------
# imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(uampl,self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2)),self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2))**2.
imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(uampl,self.ngrid,self.ngrid)),self.ngrid,self.ngrid))**2.
if (self.sflag > 0): # exact seeing blur
filter2 = np.exp(-2.*np.pi**2*(self.seeing/2.35/self.asperpix/2/self.ngrid)**2*self.r**2) # unbinned image
imh = np.abs(np.fft2(ztools.shift(np.fft2(imh),self.ngrid,self.ngrid)*filter2))
impix = ztools.rebin(imh,(self.fovpix,self.fovpix)) # rebinning into CCD pixels
else:
rr = ztools.shift(ztools.dist(self.fovpix),self.fovpix/2,self.fovpix/2)
filter2 = np.exp(-2.*np.pi**2*(self.seeing/2.35/self.ccdpix/self.fovpix)**2*rr**2) # binned image
impix = ztools.rebin(imh,[self.fovpix,self.fovpix]) # rebinning into CCD pixels
impix = np.abs(np.fft.fft2(ztools.shift(np.fft.fft2(impix),self.fovpix/2,self.fovpix/2)*filter2)) # Seeing blur
self.filter2 = filter2
return impix/np.sum(impix)
def __init__(self,cambfile='',N=500,L=1.,seed=626): kPk = numpy.loadtxt(cambfile) k,Pk = zip(*kPk) kPkf = scipy.interpolate.interp1d(k,Pk,bounds_error=False,fill_value=0.) kx = map(abs,numpy.fft.fftfreq(N)) ky = map(abs,numpy,fft.fftfreq(N)) rnd = TRandom3(seed) delta_R = [ [ rnd.Gaus(0,1) for kx_ in kx ] for ky_ in ky ] delta_F = numpy.fft2(delta_R) A_F = [ [ kPkf(math.sqrt(kx_**2+ky_**2)) for kx_ in kx ] for ky_ in ky ] for i_ in xrange(N): for j_ in xrange(N): delta_F[i_][j_] *= A_F[i_][j_]/sum(A_F[0]) delta_M = numpy.fft.ifft2(delta_F) self.N = N self.L = L self.k = k self.Pk = Pk self.delta_M = delta_M
def newimage(self, a, jzer):
'''
a is the amplitude change of aberration (micron), Jzer is the Zernike number
(1=seeing, 4=focus etc.)
:param a:
:param jzer:
:return:
'''
#COMMON imagedata, uampl, filter2, seeing
newampl = np.array(self.uampl, copy=True)
if (jzer > 1): # Change Zernike coefficient
newphase = 2. * np.pi / self.alambda * a * ztools.zernike_estim(
jzer, self.zgrid)
tmp = np.zeros_like(newphase, dtype=np.complex)
tmp += np.cos(newphase)
tmp += np.sin(newphase) * np.complex(0., 1.)
newampl[self.inside] *= tmp
filter = self.filter2
else: # new seeing
newseeing = self.seeing + a
if (self.sflag > 0):
filter = np.exp(
-2. * np.pi**2 *
(newseeing / 2.35 / self.asperpix / 2 / self.ngrid)**2 *
self.r**2) # unbinned image
else:
rr = ztools.shift(ztools.dist(self.fovpix), self.fovpix / 2,
self.fovpix / 2)
filter = np.exp(
-2. * np.pi**2 *
(newseeing / 2.35 / self.ccdpix / self.fovpix)**2 *
rr**2) # binned image
#--------- compute the image ----------------------
imh = np.abs(
ztools.shift(
np.fft.ifft2(ztools.shift(newampl, self.ngrid, self.ngrid)),
self.ngrid, self.ngrid))**2
# imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(newampl,self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2)),self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2))**2.
if (self.sflag > 0): # exact seing blur
imh = np.abs(
np.fft2(
ztools.shift(np.fft.fft2(imh), self.ngrid, self.ngrid) *
filter))
impix = ztools.rebin(
imh, [self.fovpix, self.fovpix]) # rebinning into CCD pixels
else:
impix = ztools.rebin(
imh, [self.fovpix, self.fovpix]) # rebinning into CCD pixels
impix = np.abs(
np.fft.fft2(
ztools.shift(np.fft.fft2(impix), self.fovpix / 2,
self.fovpix / 2) * filter)) # Seeing blur
return impix / np.sum(impix)
def scale_image_2d(image, factor):
"""Scales up the image by the scaling factor. No cropping is done.
Input:
image
factor"""
size_x = image.shape[0]
size_y = image.shape[1]
center_x = size_x/2
center_y = size_y/2
window_x = int(size_x/factor)
window_y = int(size_y/factor)
image_ft = _numpy.fft2(image[center_x-window_x/2:center_x+window_x/2,
center_y-window_y/2:center_y+window_y/2])
image_scaled = abs(_numpy.fft.ifftn(_numpy.fft.fftshift(image_ft), [size_x, size_y]))
return image_scaled
def HT_y(y, fft_BT, sf, sz):
[ch, n] = y.shape
s0 = sf / 2
if ch == 1:
z = zeros(sz)
z[s0:sf:end, s0:sf:end] = reshape(y, floor(sz / sf))
z = np.real(np.ifft2(np.fft2(z) * fft_BT))
z = z[:]
else:
z = np.zeros([ch, n * sf**2])
t = np.zeros(sz)
for i in range(0, ch):
t[::8, ::8] = np.reshape(y[i, :], (np.asarray(sz, dtype=int) /
sf).astype(np.int))
Htz = np.real(np.fft.ifft2(np.fft.fft2(t) * fft_BT))
z[i, :] = np.reshape(Htz, Htz.shape[0] * Htz.shape[1])
return z
def newimage(self, a, jzer):
'''
a is the amplitude change of aberration (micron), Jzer is the Zernike number
(1=seeing, 4=focus etc.)
:param a:
:param jzer:
:return:
'''
#COMMON imagedata, uampl, filter2, seeing
newampl = np.array(self.uampl,copy=True)
if (jzer > 1): # Change Zernike coefficient
newphase = 2.*np.pi/self.alambda*a*ztools.zernike_estim(jzer,self.zgrid)
tmp = np.zeros_like(newphase,dtype=np.complex)
tmp += np.cos(newphase)
tmp += np.sin(newphase)*np.complex(0.,1.)
newampl[self.inside] *= tmp
filter = self.filter2
else: # new seeing
newseeing = self.seeing + a
if (self.sflag > 0):
filter = np.exp(-2.*np.pi**2*(newseeing/2.35/self.asperpix/2/self.ngrid)**2*self.r**2) # unbinned image
else:
rr = ztools.shift(ztools.dist(self.fovpix),self.fovpix/2,self.fovpix/2)
filter = np.exp(-2.*np.pi**2*(newseeing/2.35/self.ccdpix/self.fovpix)**2*rr**2) # binned image
#--------- compute the image ----------------------
imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(newampl,self.ngrid,self.ngrid)),self.ngrid,self.ngrid))**2
# imh = np.abs(ztools.shift(np.fft.ifft2(ztools.shift(newampl,self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2)),self.ngrid+self.fovpix/2,self.ngrid+self.fovpix/2))**2.
if (self.sflag > 0): # exact seing blur
imh = np.abs(np.fft2(ztools.shift(np.fft.fft2(imh),self.ngrid,self.ngrid)*filter))
impix = ztools.rebin(imh,[self.fovpix,self.fovpix]) # rebinning into CCD pixels
else:
impix = ztools.rebin(imh,[self.fovpix,self.fovpix]) # rebinning into CCD pixels
impix = np.abs(np.fft.fft2(ztools.shift(np.fft.fft2(impix),self.fovpix/2,self.fovpix/2)*filter)) # Seeing blur
return impix/np.sum(impix)
